The implementation feasibility of control algorithms over very large-scale networks calls for hard constraints regarding communication, computational, and memory requirements. In this paper, the decentralized receding horizon control problem for very large-scale networks of dynamically decoupled systems with a common, possibly time-varying, control objective is addressed. Each system is assumed to be modeled by linear time-varying dynamics, which can be leveraged to approximate nonlinear systems about successive points of operation. A distributed and decentralized receding horizon control solution is put forward, which: (i) takes communication delays into account; (ii) allows local communication exclusively; and (iii) whose computational and memory requirements in each computational unit do not scale with the dimension of the network. The scalability of the proposed solution enables emerging very large-scale applications of swarm robotics and networked control. This approach is applied to the orbit control problem of low Earth orbit mega-constellations, featuring high-fidelity numerical simulations for the Starlink mega-constellation.

@article{PedrosoBatista2023DistributedRHC,
author = {Leonardo Pedroso and Pedro Batista},
title = {Distributed decentralized receding horizon control for very large-scale networks with application to satellite mega-constellations},
journal = {Control Engineering Practice},
year = {2023},
volume = {141},
pages = {105728},
doi = {10.1016/j.conengprac.2023.105728}
}

The design of a decentralized and distributed filtering solution for large-scale networks of interconnected systems is addressed considering (i) generic nonlinear dynamics and (ii) generic coupled nonlinear outputs in a generic, possibly time-varying, topology. The local filters, which follow the structure of the extended Kalman filter, are implemented in each system, which estimates its own state exclusively. To be suitable for the heavily restricted implementation to very large-scale systems, a novel algorithm is proposed, which: (i) does not rely on instantaneous data transmission; (ii) allows local communication exclusively; and (iii) requires computational, memory, and data transmission resources for each system that do not scale with the dimension of the network. The scalability of the proposed algorithm allows for its application to the cooperative localization problem of very large-scale systems. In particular, it is applied herein to the on-board position estimation problem of LEO mega-constellations using GNSS featuring numerical simulations for the Starlink constellation.

@article{PedrosoBatista2023DistributedEKF,
author = {Leonardo Pedroso and Pedro Batista},
title = {Distributed decentralized {EKF} for very large-scale networks with application to satellite mega-constellations navigation},
journal = {Control Engineering Practice},
year = {2023},
volume = {135},
pages = {105509},
doi = {10.1016/j.conengprac.2023.105509}
}

This paper addresses the problem of designing a decentralized state estimation solution for a large-scale network of interconnected unconstrained linear time invariant (LTI) systems. The problem is tackled in a novel moving horizon estimation (MHE) framework, while taking into account the limited communication capabilities and the restricted computational power and memory, which are distributed across the network. The proposed design is motivated by the fact that, in a decentralized setting, a Luenberguer-based framework is unable to leverage the full potential of the available local information. A method is derived to solve a relaxed version of the resulting optimization problem. It can be synthesized offline and its stability can be assessed prior to deployment. It is shown that the proposed approach allows for significant improvement on the performance of recent Luenberger-based filters. Furthermore, we show that a state-of-the-art distributed MHE solution with comparable requirements underperforms in comparison to the proposed solution.

@article{PedrosoBatista2023DecentralizedMHE,
author = {Leonardo Pedroso and Pedro Batista},
title = {Decentralized moving horizon estimation for large-scale networks of interconnected unconstrained linear systems},
journal = {IEEE Transactions on Control of Network Systems},
year = {2023},
volume = {10},
number = {4},
pages = {1855-1866},
doi = {10.1109/TCNS.2023.3244086}
}

This article addresses the problem of designing a decentralized control solution for a network of agents modeled by linear time-varying (LTV) dynamics, in a discrete-time framework. A general scheme is proposed, in which the problem is formulated as a classical linear quadratic regulator problem, for the global system, subject to a given sparsity constraint on the gain, which reflects the decentralized nature of the network. A method able to compute a sequence of well-performing stabilizing regulator gains is presented and validated resorting to simulations of two randomly generated LTV systems, one stable and the other unstable. Moreover, a tracking solution is developed, building on the solution to the regulator problem. Both methods rely on a closed-form solution, thus they can be computed very rapidly. Similarly to the centralized solution, both the presented methods require that a window of the future system dynamics is known. Both methods are validated resorting to simulations of: (i) a nonlinear network of four interconnected tanks; and (ii) a large-scale nonlinear network of interconnected tanks. When implemented to a nonlinear network, approximated by an LTV system, the proposed methods are able to compute well-performing gains that track the desired output. Finally, both algorithms are scalable, being adequate for implementation in large-scale networks.

@article{PedrosoBatista2023DecentralizedLQR,
author = {Leonardo Pedroso and Pedro Batista},
title = {Discrete-time decentralized linear quadratic control for linear time-varying systems},
journal = {International Journal of Robust and Nonlinear Control},
year = {2023},
volume = {33},
number = {1},
pages = {67-101},
doi = {10.1002/rnc.5772}
}

The major hurdle in accessing laboratory experimentation is the cost of acquiring experimental scientific equipment, which is unbearable for many institutions. This paper aims to provide the community of control educators, practitioners, and researchers with an open-source low-cost experimental setup and dedicated interface, which is flexible and very easily reproducible. The proposed apparatus is a setup of four interconnected tanks. The setup is representative of real-life industrial processes and it can be adjusted to allow for several configurations for flexibility. A user-friendly dedicated MATLAB/Simulink interface with a personal computer is developed. It supports a seamless shift between a numeric simulation of the quadruple-tank process dynamics and the interface with the physical experimental plant. The CAD models, technical drawings, wiring schematics, PCB design, interface, assembly tutorials, and several examples are provided in an open-source repository. The parts are inexpensive, readily obtained, and fast to assemble. Each setup costs under 650€ and takes roughly 4 h to assemble. In this paper, several application examples are presented, not only for educational purposes, but also for the validation of a state-of-the-art decentralized control method.

@article{PedrosoBatista2022Quadruple-tank,
author = {Leonardo Pedroso and Pedro Batista},
title = {Reproducible low-cost flexible quadruple-tank process experimental setup for control educators, practitioners, and researchers},
journal = {Journal of Process Control},
year = {2022},
volume = {118},
pages = {82-94},
doi = {10.1016/j.jprocont.2022.08.010}
}

This paper addresses the problem of designing distributed state estimation solutions for a network of interconnected systems modelled by linear time-varying (LTV) dynamics in a discrete-time framework. The problem is formulated as a classical optimal estimation problem, for the global system, subject to a given sparsity constraint on the filter gain, which reflects the distributed nature of the network. Two methods are presented, both of them able to compute a sequence of well-performing stabilising gains. Moreover, both methods are validated by resorting to simulations of: (i) a randomly generated synthetic LTV system; and (ii) a large-scale nonlinear network of interconnected tanks. One of the proposed methods relies on a computationally efficient solution, thus it is computed very rapidly. The other achieves better performance, but it is computationally more expensive and requires that a window of the future dynamics of the system is known. When implemented to a nonlinear network, approximated by an LTV system, the proposed methods are able to compute well-performing gains that stabilise the estimation error dynamics. Both algorithms are scalable, being adequate for implementation in large-scale networks.

@article{PedrosoBatistaEtAl2022DistributedKalman,
author = {Leonardo Pedroso and Pedro Batista and Paulo Oliveira and Carlos Silvestre},
title = {Discrete-time distributed Kalman filter design for networks of interconnected systems with linear time-varying dynamics},
journal = {International Journal of Systems Science},
year = {2022},
volume = {53},
number = {6},
pages = {1334-1351},
doi = {10.1080/00207721.2021.2002461}
}

This paper aims to explore a new technique for structural damage identification using cubic spline interpolation. The method is based on the interpolation of modal rotations measured with shearography, making use of the analytical derivative of the spline to compute the modal curvature, which is known to be very sensitive to damage. As a means of reducing noise and measurement uncertainty propagation to a minimum, an expression for an optimal spatial sampling is derived. Furthermore, a baseline-free damage factor, allied with an optimal sampling, is also introduced. The proposed identification method is validated using experimental data of a beam. Using a damage localisation quality index, a comparison between the present method and one using finite differences is carried out, showing that the differentiation of spline interpolation leads to better damage identifications. The results obtained with the proposed approach show robustness and consistency in the localisations. Additionally, the hurdles of identifying small and multiple damage are tackled with the proposed method, yielding a good performance.

@article{PedrosoArcoEtAl2022Spline,
author = {Leonardo Pedroso and António Arco and Iara Figueiras and J. V. A. dos Santos and J. L. M. Fernandes and Hernâni Lopes},
title = {Application of cubic spline interpolation with optimal spatial sampling for damage identification},
journal = {Structural Control and Health Monitoring},
year = {2022},
volume = {29},
number = {1},
pages = {e2856},
doi = {10.1002/stc.2856}
}

Signal control strategies for congested urban road networks designed in a centralized framework require many communication links, serious processing power, and infrastructure for the centralized coordination. As a result, strategies based on a centralized framework are not scalable. The use of decentralized signal control strategies for large-scale urban traffic networks is a solution to this problem, since it allows for the implementation of such strategies on networks whose centralized solution is not easily scalable. This paper addresses the problem of designing a decentralized traffic-responsive signal control solution, proposing two methods based on different formulations of the store-and-forward model: (i) the Decentralized Traffic-responsive Urban Control (DTUC) method; and (ii) the Decentralized Decoupled Traffic-responsive Urban Control (D2TUC). The decentralized configuration is such that each intersection is associated with one computational unit, with limited computational power and memory, which controls the traffic signals of the incoming links. Sufficient conditions for the controllability of the considered store-and-forward models are also presented. Both methods are validated resorting to numerical simulations of the urban traffic network of Chania, Greece, for two demand scenarios, and their performance is compared with the performance of the Traffic-responsive Urban Control (TUC) centralized strategy. One of the proposed decentralized methods, D2TUC, is shown to match the performance of TUC.

@article{PedrosoBatista2021SignalControl,
author = {Leonardo Pedroso and Pedro Batista},
title = {Decentralized store-and-forward based strategies for the signal control problem in large-scale congested urban road networks},
journal = {Transportation Research Part C: Emerging Technologies},
year = {2021},
volume = {132},
pages = {103412},
doi = {10.1016/j.trc.2021.103412}
}

In this short communication, an algorithm for efficiently solving a sparse matrix equation, which arises frequently in the field of distributed control and estimation theory, is proposed. The efficient algorithm stems from the fact that the sparse equation at hand can be reduced to a system of linear equations. The proposed algorithm is shown to require significantly fewer floating point operations than the state-of-the-art solution. The proposed solution is applied to a real-life example, which models a wide range of industrial processes. The experimental results show that the solution put forward allows for a significant increase in efficiency in relation to the state-of-the-art solution. The significant increase in efficiency of the presented algorithm allows for a valuable widening of the applications of distributed estimation and control.

@article{PedrosoBatista2021SparseEquation,
author = {Leonardo Pedroso and Pedro Batista},
title = {Efficient Algorithm for the Computation of the Solution to a Sparse Matrix Equation in Distributed Control Theory},
journal = {Mathematics},
year = {2021},
volume = {9},
number = {13},
doi = {10.3390/math9131497}
}

Research on the operation of mobility systems so far has mostly focused on minimizing cost-centered metrics such as average travel time, distance driven, and operational costs. Whilst capturing economic indicators, such metrics do not account for transportation justice aspects. In this paper, we present an optimization model to plan the operation of Intermodal Autonomous Mobility-on-Demand (I-AMoD) systems, where self-driving vehicles provide on-demand mobility jointly with public transit and active modes, with the goal to minimize the accessibility unfairness experienced by the population. Specifically, we first leverage a previously developed network flow model to compute the I-AMoD system operation in a minimum-time manner. Second, we formally define accessibility unfairness, and use it to frame the minimum-accessibility-unfairness problem and cast it as a linear program. We showcase our framework for a real-world case-study in the city of Eindhoven, NL. Our results show that it is possible to reach an operation that is on average fully fair at the cost of a slight travel time increase compared to a minimum-travel-time solution. Thereby we observe that the accessibility fairness of individual paths is, on average, worse than the average values obtained from flows, setting the stage for a discussion on the definition of accessibility fairness itself.

@misc{SalazarBetancurEtAl2024Acc,
author = {Mauro Salazar and Sara Betancur Giraldo and Fabio Paparella and Leonardo Pedroso},
title = {On Accessibility Fairness in Intermodal Autonomous Mobility-on-Demand Systems},
note = {arXiv preprint arXiv:2404.00434},
year = {2024},
doi = {10.48550/arXiv.2404.00434}
}

When users access shared resources in a selfish manner, the resulting societal cost and perceived users' cost is often higher than what would result from a centrally coordinated optimal allocation. While several contributions in mechanism design manage to steer the aggregate users choices to the desired optimum by using monetary tolls, such approaches bear the inherent drawback of discriminating against users with a lower income. More recently, incentive schemes based on artificial currencies have been studied with the goal of achieving a system-optimal resource allocation that is also fair. In this resource-sharing context, this paper focuses on repeated weighted congestion game with two resources, where users contribute to the congestion to different extents that are captured by individual weights. First, we address the broad concept of fairness by providing a rigorous mathematical characterization of the distinct societal metrics of equity and equality, i.e., the concepts of providing equal outcomes and equal opportunities, respectively. Second, we devise weight-dependent and time-invariant optimal pricing policies to maximize equity and equality, and prove convergence of the aggregate user choices to the system-optimum. In our framework it is always possible to achieve system-optimal allocations with perfect equity, while the maximum equality that can be reached may not be perfect, which is also shown via numerical simulations.

@misc{PedrosoAgazziEtAl2024EqtEql,
author = {Leonardo Pedroso and Andrea Agazzi and W. P. M. H. Heemels and Mauro Salazar},
title = {Fair Artificial Currency Incentives in Repeated Weighted Congestion Games: Equity vs. Equality},
note = {arXiv preprint arXiv:2403.03999},
year = {2024},
doi = {10.48550/arXiv.2403.03999}
}

To cope with varying and highly uncertain traffic patterns, a novel network-wide traffic signal control strategy based on the store-and-forward model of a traffic network is proposed. On one hand, making use of a single loop detector in each road link, we develop an estimation solution for both the link occupancy and the net exogenous demand in every road link of a network. On the other hand, borrowing from optimal control theory, we design an optimal linear quadratic control scheme, consisting of a linear feedback term, of the occupancy of the road links, and a feedforward component, which accounts for the varying exogenous vehicle load on the network. Thereby, the resulting control scheme is a simple feedback-feedforward controller, which is fed with occupancy and exogenous demand estimates, and is suitable for real-time implementation. Numerical simulations of the urban traffic network of Chania, Greece, show that, for realistic surges in the exogenous demand, the proposed solution significantly outperforms tried-and-tested solutions that ignore the exogenous demand.

@misc{PedrosoBatistaEtAl2023FeedbackFeedforward,
author = {Leonardo Pedroso and Pedro Batista and Markos Papageorgiou},
title = {Feedback-feedforward Signal Control with Exogenous Demand Estimation in Congested Urban Road Networks},
note = {arXiv preprint arXiv:2312.07359},
year = {2023},
doi = {10.48550/arXiv.2312.07359}
}

This paper presents a framework to incorporate ride-pooling from a mesoscopic point of view, within time-invariant network flow models of Mobility-on-Demand systems. The resulting problem structure remains identical to a standard network flow model, a linear problem, which can be solved in polynomial time for a given ride-pooling request assignment. In order to compute such a ride-pooling assignment, we devise a polynomial-time knapsack-like algorithm that is optimal w.r.t. the minimum user travel time instance of the original problem. Finally, we conduct two case studies of Sioux Falls and Manhattan, where we validate our models against state-of-the-art time-varying results, and we quantitatively highlight the effects that maximum waiting time and maximum delay thresholds have on the vehicle hours traveled, overall pooled rides and actual delay experienced. We show that for a sufficient number of requests, with a maximum waiting time and delay of 5 minutes, it is possible to ride-pool more than 80% of the requests for both case studies. Last, allowing for four people ride-pooling can significantly boost the performance of the system.

@misc{PaparellaPedrosoEtAl2023Ride-pooling,
author = {Fabio Paparella and Leonardo Pedroso and Theo Hofman and Mauro Salazar},
title = {A Time-invariant Network Flow Model for Ride-pooling in Mobility-on-Demand Systems},
note = {arXiv preprint arXiv:2311.06035},
year = {2023},
doi = {10.48550/arXiv.2311.06035}
}

This paper presents a modeling and optimization framework to study congestion-aware ride-pooling Autonomous Mobility-on-Demand (AMoD) systems, whereby self-driving robotaxis are providing on-demand mobility, and users headed in the same direction share the same vehicle for part of their journey. Specifically, taking a mesoscopic time-invariant perspective and on the assumption of a large number of travel requests, we first cast the joint ride-pooling assignment and routing problem as a quadratic program that does not scale with the number of demands and can be solved with off-the-shelf convex solvers. Second, we compare the proposed approach with a significantly simpler decoupled formulation, whereby only the routing is performed in a congestion-aware fashion, whilst the ride-pooling assignment part is congestion-unaware. A case study of Sioux Falls reveals that such a simplification does not significantly alter the solution and that the decisive factor is indeed the congestion-aware routing. Finally, we solve the latter problem accounting for the presence of user-centered private vehicle users in a case study of Manhattan, NYC, characterizing the performance of the car-network as a function of AMoD penetration rate and percentage of pooled rides within it. Our results show that AMoD can significantly reduce congestion and travel times, but only if at least 40% of the users are willing to be pooled together. Otherwise, for higher AMoD penetration rates and low percentage of pooled rides, the effect of the additional rebalancing empty-vehicle trips can be even more detrimental than the benefits stemming from a centralized routing, worsening congestion and leading to an up to 15% higher average travel time.

@inproceedings{PaparellaPedrosoEtAl2024Congestion,
author = {Fabio Paparella and Leonardo Pedroso and Theo Hofman and Mauro Salazar},
title = {Congestion-aware Ride-pooling in Mixed Traffic for Autonomous Mobility-on-Demand Systems},
booktitle = {2024 European Control Conference (ECC)},
year = {2024},
doi = {10.48550/arXiv.2311.03268},
note = {in press}
}

Within mobility systems, the presence of self-interested users can lead to aggregate routing patterns that are far from the societal optimum which could be achieved by centrally controlling the users' choices. In this paper, we design a fair incentive mechanism to steer the selfish behavior of the users to align with the societally optimal aggregate routing. The proposed mechanism is based on an artificial currency that cannot be traded or bought, but only spent or received when traveling. Specifically, we consider a parallel-arc network with a single origin and destination node within a repeated game setting whereby each user chooses from one of the available arcs to reach their destination on a daily basis. In this framework, taking faster routes comes at a cost, whereas taking slower routes is incentivized by a reward. The users are thus playing against their future selves when choosing their present actions. To capture this complex behavior, we assume the users to be rational and to minimize an urgency-weighted combination of their immediate and future discomfort. To design the optimal pricing, we first derive a closed-form expression for the best individual response strategy. Second, we formulate the pricing design problem for each arc to achieve the societally optimal aggregate flows, and reformulate it so that it can be solved with gradient-free optimization methods. Our numerical simulations show that it is possible to achieve a near-optimal routing whilst significantly reducing the users' perceived discomfort when compared to a centralized optimal but urgency-unaware policy.

@inproceedings{PedrosoHeemelsEtAl2023KarmaParallel,
author = {Leonardo Pedroso and W. P. M. H. Heemels and Mauro Salazar},
title = {Urgency-aware Routing in Single Origin-destination Itineraries through Artificial Currencies},
booktitle = {62nd IEEE Conference on Decision and Control},
year = {2023},
pages = {4142-4149},
doi = {10.1109/CDC49753.2023.10383739}
}

This paper presents a time-invariant network flow model capturing two-person ride-pooling that can be integrated within design and planning frameworks for Mobility-on-Demand systems. In these type of models, the arrival process of travel requests is described by a Poisson process, meaning that there is only statistical insight into request times, including the probability that two requests may be pooled together. Taking advantage of this feature, we devise a method to capture ride-pooling from a stochastic mesoscopic perspective. This way, we are able to transform the original set of requests into an equivalent set including pooled ones which can be integrated within standard network flow problems, which in turn can be efficiently solved with off-the-shelf LP solvers for a given ride-pooling request assignment. Thereby, to compute such an assignment, we devise a polynomial-time algorithm that is optimal w.r.t. an approximated version of the problem. Finally, we perform a case study of Sioux Falls, USA, where we quantify the effects that waiting time and experienced delay have on the vehicle-hours traveled. Our results suggest that the higher the demands per unit time, the lower the waiting time and delay experienced by users. In addition, for a sufficiently large number of demands per unit time, with a maximum waiting time and experienced delay of 5 minutes, more than 90% of the requests can be pooled.

@inproceedings{PaparellaPedrosoEtAl2023TwoRide-pooling,
author = {Fabio Paparella and Leonardo Pedroso and Theo Hofman and Mauro Salazar},
title = {A Time-invariant Network Flow Model for Two-person Ride-pooling Mobility-on-Demand},
booktitle = {62nd IEEE Conference on Decision and Control},
year = {2023},
pages = {4118-4123},
doi = {10.1109/CDC49753.2023.10384279}
}

The SAFFRON toolbox is introduced to synthesize, analyze, and simulate store-and-forward based strategies for the signal control problem in congested urban road networks in MATLAB. It features: i) well-documented tools to manipulate and simulate store-and-forward macroscopic traffic network models; ii) the parameters of the model of the urban road network of the city center of Chania, Greece; and iii) the implementation of state-of-the-art signal control strategies.

@inproceedings{PedrosoBatistaEtAl2022Saffron,
author = {Leonardo Pedroso and Pedro Batista and Markos Papageorgiou and Elias Kosmatopoulos},
title = {{SAFFRON}: {Store-And-Forward} model toolbox {For} urban {ROad} {Network} signal control in {MATLAB}},
booktitle = {2022 IEEE 25th International Conference on Intelligent Transportation Systems (ITSC)},
year = {2022},
pages = {3698-3703},
doi = {10.1109/ITSC55140.2022.9922508}
}

This paper aims to explore a new technique for structural damage identification using cubic spline interpolation. The method is based on the interpolation of modal rotations measured with speckle shearography. In order to locate the damaged areas, we make use of the analytical derivative of the cubic spline function to compute the modal curvature, which is known to be very sensitive to damage. A comprehensive parametric study of the spatial sampling interval is carried out to find its influence on noise filtering. Furthermore, the identification quality dependency on the mode shape and respective noise is also examined. The results obtained with the proposed method show the consistency of the localizations. Additionally, the challenging tasks of identifying small and multiple damage are tackled, yielding a good performance.

@inproceedings{ArcoFigueirasEtAl2019Spline,
author = {António Arco and Iara Figueiras and Leonardo Pedroso and J. V. {Araújo dos Santos} and J. L. M. Fernandes and H. Lopes},
title = {Application of spline interpolation to speckle shearography measurements for damage identification},
booktitle = {3rd International Conference on Structural Integrity (ICSI 2019)},
year = {2019},
volume = {17},
pages = {718-725},
doi = {10.1016/j.prostr.2019.08.096}
}

The advantages and tremendous potential of very large-scale complex networks of interconnected systems are indisputable in a myriad of engineering fields, not only as business opportunities but also as a natural change towards efficiency, reliability, and scalability. In particular, mega-constellations of satellites promise to revolutionize the future of communications and Earth observation and monitoring. Although efforts towards the deployment of these solutions are underway, decades-old tried and tested individual ground-based tracking telemetry and command technologies condemn these ventures to practical unfeasibility and economic unviability. The goal of this thesis follows from the self-evident void in the state-of-the-art, aiming to bring these endeavors to fruition. First, the distributed and decentralized control problem is formulated in a receding horizon control framework alongside the severe large-scale feasibility constraints. Second, a convex relaxation procedure is proposed to approximate the optimal solution of the regulator synthesis problem in a decentralized setting, which is validated resorting to a large-scale numeric simulation and experimental results. Moreover, a tracking solution is put forward. Third, a novel distributed and decentralized networked control solution is developed for the particular case of dynamically decoupled systems. The controller synthesis computations are distributed across the network leveraging the proposed convex relaxation, an approximation, and a scheduling procedure, to comply with the feasibility constraints on a very large-scale. Fourth, the potential of the proposed solution is successfully illustrated for the cooperative on-board orbit control of the Starlink mega-constellation. The shape-keeping task is formulated in a novel framework with emphasis on efficiency and fuel saving.

@mastersthesis{Pedroso2022Thesis,
author = {Leonardo Pedroso},
title = {Distributed decentralized control for very large-scale systems with application to {LEO} satellite mega-constellations},
year = {2022},
school = {Instituto Superior Técnico, University of Lisbon}
}